RT Journal Article
T1 Ellis enveloping semigroups in real closed fields
A1 Baro González, Elías
A1 Palacín Cruz, Daniel
AB We introduce the Boolean algebra of d-semialgebraic (more generally, d-definable) sets and prove that its Stone space is naturally isomorphic to the Ellis enveloping semigroup of the Stone space of the Boolean algebra of semialgebraic (definable) sets. For definably connected o-minimal groups, we prove that this family agrees with the one of externally definable sets in the one-dimensional case. Nonetheless, we prove that in general these two families differ, even in the semialgebraic case over the real algebraic numbers. On the other hand, in the semialgebraic case we characterise real semialgebraic functions representing Boolean combinations of d-semialgebraic sets
YR 2024
FD 2024-01-15
LK https://hdl.handle.net/20.500.14352/108622
UL https://hdl.handle.net/20.500.14352/108622
LA eng
NO Baro E, Palacín D. Ellis enveloping semigroups in real closed fields. Rev Real Acad Cienc Exactas Fis Nat Ser A-Mat 2024;118:69. https://doi.org/10.1007/s13398-024-01562-7.
DS Docta Complutense
RD 6 abr 2025